Modeling and Tracking Control of Nondifferentiable Sandwiched Dynamic Systems: Case Study on Gear Transmission Servo Systems

Many practical engineering systems, classified as nondifferentiable sandwiched dynamic systems (NSDSs), pose significant challenges to controller design due to their inherent unknown nondifferentiable nonlinearities. Among these, gear transmission servo (GTS) systems constitute a prominent research focus, exemplifying the complexities associated with modeling and control in NSDSs. Specifically, gear backlash introduces internal dead-zone nonlinearities, causing detrimental effects such as vibrations, diminished control accuracy, and potential instability. Such systems, characterized by unknown parameters including dead-zone characteristics, form fourth-order nonlower triangular dynamic structures, further complicated by uncertainties and external disturbances that impede convergence and controller performance. To address these critical challenges, this article proposes a novel block-structured control framework (BSCF) integrating feedforward compensation, nonlinear extended state observers, and dynamic surface control techniques, all built upon system identification results. A rigorous Lyapunov-based analysis is provided to establish that the tracking error converges to a bounded neighborhood of the origin, with the ultimate bound being adjustable through suitable parameter tuning. Experimental results confirm the effectiveness of the proposed strategy in eliminating the adverse effects of dead-zone nonlinearities and achieving satisfactory tracking accuracy. Furthermore, this control framework demonstrates broad applicability and can be extended to other sandwiched systems featuring nondifferentiable nonlinearities and/or nonlower triangular structures.